Diagrid Structures: Introduction & Literature Survey

Diagrid is a structural system typically used for tall buildings. In this slide you will be introduced to diagrid system, various terminologies and current researches in diagrid structural environment.

1. Diagrid Structures Guided by : Dr. S. A. Bhalchandra , As. Prof. AMD Presented by : Uday M.

2. Introduction Firstly introduced by Vladimir Grigoryevich Shukhov as hyperboloid towers for water tanks. Then revived by Froster Nohman Consists of structure with an RCC core and grid of diagonal members around Use of perimeter diagonals—hence the term ‘diagrid’—for structural effectiveness and esthetics In late 19th century early designs of tall buildings recognized the effectiveness of diagonal bracing members in resisting lateral force Almost all the conventional vertical columns are eliminated Triangulation provides efficient load carrying system Diagonal members in diagrid structural systems can carry gravity loads as well as lateral forces

3. Carry shear by axial action of the diagonal members and lateral by bending of diagonal member Provides both bending and shear rigidity Behave like a 3-dimensional box resisting both compression and tension Diagrid structures are less prone to a lock-in condition Very effective in case of buildings up to 70-100 story

4. Why to be interested in diagrids ? 45-75 story buildings are economical hence are in abundance of the total world buildings Worlds building No. of building vs. storey India’s buildings Height of buildings vs. storey

5. Components of typical diagrid structure h is the module height of the building indicated in terms of story. Typical module is 4-6 story high H/B ratio of the building is the aspect ratio of that building

6. Tie beams transfers the load from RC core to diagrid Ring beam resists the unbalance forces

7. Connections in Diagrids Nodes are fabricated and then raised piece by piece In case of an irregular structure, each node has to designed separately Welded nodes are preferred but are time and skill demanding Bolded connections are used for speedier erections The sections used – circular or I-beam or rectangular

8. Each node joint is designed for vertical loading as well as for the lateral loading

9. Load Transfer in Diagrids Load transfer in concentrated, ULD and Lateral load Effect on triangular elements

10. Literature Review G. Subramanian & N. Subramonian (1970 ) After obtaining the partial difference equation governing the deflection of laterally loaded uniform diagrids, closed-form solutions are presented for the simply supported case. Recognizing that the above formulation for diagrids can easily be extended to study the lateral oscillations by replacing the static loads at the nodes with inertia loads, assuming masses to be lumped at the nodes, expressions are obtained for natural frequencies of vibration, for the simply supported uniform diagrids. Kyoung -Sun Moon et al (2007 ) Presents A Simple Methodology For Determining Preliminary Member Sizes Examined The Influence Of The Diagonal Angle On The Behavior Of Diagrid Type Structures For 60-story Diagrid Structures Having An Aspect Ratio Of About 7, The Optimal Range Of Diagrids Angle Is From About 65° To 75°

11. Charnish (2008) Studied various types of diagrid structures of different optimal configuration and of various aspect ratios with varying module sizes Concluded that A 20% savings in the weight of the structural steel is possible using A diagrid versus A braced tube Dong- Kyu Lee et al (2010 ) Research provides both a design and analysis tool for diagrid structural designs and diagrid structural analyses Considering both static and dynamic behaviors, appropriate diagrid is designed It is verified that diagrids are redundant and loads follow the diagonals through the structure For 42-story buildings having an aspect ratio of about 5, the range is lower by around 10° because the importance of bending to the total lateral displacement is reduced as the building height decreases A stiffness-based methodology for determining preliminary design sizes for the diagonals was introduced

12. T. M. Boak (2010) Diagrids are displaying a language of detailing and design that corresponds to choices in the size of the base module, building type and three-dimensional geometry of the project. Diagrids are demonstrating a dynamic and adaptable structural system that is more adapt at structuring contemporary architectural aspirations Considering shape or sizing optimization problems, the number of movable design variables is relatively very large also some supports may be linked in order to keep the structural system symmetric or limit the number of design variables treated, hence the dynamics-based optimization model is developed to find natural frequency of the system Once the fundamental frequency oscillates with topology movements, the material interpolation technique, called the penalty law or SIMP will be used to estimate the optimal topology within the element

13. Moon et al (2011 ) Analyzed the twisted structures, tilted towers and freeform complex structures For A typical study, in twisted towers and tilted tower analysis, deflection at top in diagrid structures were about 8-10% lesser More effective at more twist rates and leaning, shows more stiffness Raghunath .d. Deshpande et al (2015 ) diagrid performs better across all the criterions of performance evaluation, such as, efficiency, expressiveness and sustainability. Diagrid structure have comparatively less deflection. Their structural weight is reduced to greater extent. Due to this structure has more resistance to lateral forces. Diagrid structures are cost effective and eco-friendly. Diagrid uses 11247 tonnes of steel which is 28% less compared to the conventional orthogonal building which uses 15255 tonnes.

14. Rohit Kumar Singh et al.(2014 ) A regular five storey RCC building with plan size 15 m × 15 m located in seismic zone v is considered for analysis. diagrid building shows less lateral displacement and drift in comparison to conventional building although volume of concrete used in both building is approx. same, but diagrid shows more economical in terms of steel used. Diagrid building saves about 33% steel without affecting the structural efficiency Better resistance to lateral loads: due to diagonal columns on its periphery, diagrid shows better resistance to lateral loads and due to this, inner columns get relaxed and carry only gravity loads . While in conventional building both inner and outer column are designed for both gravity and lateral loads, In diagrids only columns are designed to resist both.

15. Design Methodology There are three ways to design diagrid structures PDE method governing the deflection using the slope deflection equations Optimization Technique Stiffness Based Methodology

16. A. PDE method governing the deflection using the slope deflection equations After obtaining the partial difference equation governing the deflection of laterally loaded uniform diagrids, closed-form solutions are presented for the simply supported case. Recognizing that the above formulation for diagrids can easily be extended to study the lateral oscillations by replacing the static loads at the nodes with inertia loads, assuming masses to be lumped at the nodes, expressions are obtained for natural frequencies of vibration, for the simply supported uniform diagrids. Investigation revealed that at least for the case of simple supports on all edges, the lowest natural frequencies are closely approximated by the lumped mass approximation.

17. Rectangular diagrid with 45 degree angle

18. Consider an R beam extending from (r, s) to (r+ l, s+ 1) the slope deflection equations for the (r+ l) th span of an R beam may be written as Also the equations for Shear and Torque are developed Applying equations of equilibriums as

19. Solving and using a shift operator Er and Es Substituting back in equations of slope deflection Substituting in equilibrium equations and solving

20. The obtained value is then used in an explicit formula for the determination of frequencies. The allowable values for k are l, 2……..m-1 and for l are l , 2…....... n-1; Beyond these, values for frequencies merely repeat themselves. Thus, fundamental frequency can be determined

21. It consists of two methodologies To evaluate desired angles of diagonal members consisting of diagrid with respect to stiffness of optimal topology To investigate or understand global and topological diagrid mechanism by using topology optimization technique dynamics-based optimization model is, in general, written as max: ωi ( i =1, ..., m) subject to ajj ≤ aj ≤ aji (j=1,…,n) ad = f ( aj ) aj denotes the design variable, representing the j- th independent finite element and ad is an arbitrary value which derives a dynamic governing function f depending on aj into zero. aj and aj denote the lower (almost 0 for voids) and upper (1 for solids) bounds of the design variable, respectively In general, maximization of the first-order Eigen-frequency is taken into account as objective, since structure with 1 st Eigen-mode has a tendency to the weakest stiffness B. Optimization Technique

22. To execute the optimization procedure, the FE method is utilized as an analyzer to calculate the natural frequency and associated vibration mode Once the fundamental frequency oscillates with topology movements, the material interpolation technique, called the penalty law or SIMP will be used to estimate the optimal topology In order to yield the optimum position model of fixed support models for distributing material density, sensitivity derivatives need to be studied Finally using minimum energy as constraints, optimal topology boundaries are determined

23. For tall buildings with a large height-to-width aspect ratio, the stiffness constraint generally governs the design Important stiffness design parameters to consider in any tall building design is its maximum deflection which is usually five hundredth of the building height Diagrid structure is modeled as a vertical cantilever beam on the ground, and subdivided longitudinally into modules In order to more accurately estimate the lateral rigidity provided by diagrids, all the required lateral stiffness is allocated to the perimeter diagrids The diagonal members are assumed to be pin-ended, and therefore resist the transverse shear and moment through axial action only – idealization Areas of diagonals on flange and web side are given as-   3. Stiffness Based Methodology

24. Optimal stiffness-based design corresponds to a state of uniform shear and bending deformation under the design loading Since Uniform deformation states are possible only for statically determinate structures and Tall building structures can be modeled as vertical cantilever beams on the ground, and uniform deformation can be achieved for these structures Deflection at the top, u(H) is given by H: Building Height : Desired Uniform Transverse Shear Strain : Desired Uniform Curvature In order to specify the relative contribution of shear versus bending deformation, a dimensionless factor ‘s ’  

25. The maximum allowable displacement, one of the most important stiffness-based design parameters for tall buildings, is usually expressed as a fraction of the total building height For Lateral Loading, introduce a dimensionless factor f, which is defined as the ratio of the strain in a web diagonal due to shearing action to the strain in a flange diagonal due to bending action Where, and For braced frame, f > 1 (3 to 6) and for diagrid f < 1  

26. Relationship between Aspect ratios to that of s and f Based on these studies, the following empirical relationship between the optimal s value and the aspect ratio is proposed for diagrid structures greater than 40 stories with an aspect ratio greater than about 5 and a diagrid angle between 60° and 70 °.  

27. Optimal angle of diagonal members Considering only the maximum shear rigidity, the optimal angle for diagonal members can be estimated using key assumption that the members carry only axial forces The cross-section shear force is related to the diagonal member forces by: V = 2 F d cosθ Assuming linear elastic behavior, the member forces are also related to the diagonal extensional strain, ɛd , by F d = A d σ d = A d E d ɛ d And extensional strain is given by – V = D T x axial strain deformation due to shear : . D T = A D E D sin2θ cosθ

28. The plot of sin 2θ cosθ is s that the optimal angle for maximum shear rigidity of the system is about 35 ° In typical braced frames, the bending moment is carried by the axial forces in the vertical columns i.e. maximum rigidity at 90° optimal angle of the diagonal members of diagrid structures will fall between these angles

29. 1. Diagrids of Uniform Angle For a preliminary design 60 story building with various uniform angle configuration is considered Experimental Case Studies: Case Study - I - Kyoung S. Moon (2007)

30. With Corner Columns Without Corner Columns

31. With Corner Columns Without Corner Columns

32. Relative stiffness of diagrid and braced core

33. Preliminary sizes of the diagrid for 60 story and 42 story building

34. Height (Aspect Ratio) Near Optimal Uniform Angle Near Optimal ‘s’ 40 Stories (4.3) 63 Degrees 4 50 Stories (5.4) 63 Degrees 6 60 Stories (6.5) 69 Degrees 4 70 Stories (7.6) 69 Degrees 5 80 Stories (8.7) 69 Degrees 6 Story Module Diagrid Angle Diagrid Steel Mass (Ton) Percentile Difference 2 stories 52 degrees 5700 +50.0% 3 stories 63 degrees 3930 +3.4% 4 stories 69 degrees 3800 Near Optimal 5 stories 73 degrees 4200 +5.3% 6 stories 76 degrees 4960 +30.5% Masses has calculated and proves that the angle is optimal Different buildings with this optimal angle

35. 2. Diagrids of Varying Angle Diagrid structure having varying angles of 63, 69, and 73 degrees from the top to the bottom, uniform and bottom to top are analyzed For more height the value of ‘s’ is more sensitive Diagrid Height ( Aspect Ratio) Diagrid Angles ( Top to Bottom) Near Optimal ‘s’ 60 Stories (6.5) 63, 69, and 73 Degrees 2.2 70 Stories (7.6) 63, 69, and 73 Degrees 4.2 80 Stories (8.7) 63, 69, and 73 Degrees 4.9

36. For a typical 60 story building but with various values of s, different optimal parameters are obtained. S = 1 S = 8 S = 4

37. Comparison of uniform and varying angle diagrids Case Alt. Angle Description Optimal 's' Steel Mass (tons) 1 2 76 , 73, 69, 63,52 0.9 1068   1 69 , 63, 52 2.7 1009 Uniform Angle   63 4.1 883 2 1 52, 63, 69 5.1 1906   2 52, 63 , 69, 73, 76 2.1 1597 For a 40 story building with varying angles and varying geometrical positions, optimum steel is computed

38. Case Alt. Angle Description Optimal 's' Steel Mass (tons) 1 2 79, 76, 73, 69, 63 0.9 5791   1 73, 69, 63 2.2 4104 uniform Angle   69 3.9 3820   2 1 63, 69, 73 3.7 4482 2 63, 69, 73, 76, 79 1.4 6549 For a 60 story building with varying angles and varying geometrical positions, optimum steel is computed

39. - R. D . Deshpande et al. DESCRIPTION VALUE Height 180m Width 24m(Square plan) Core wall dimension 12mx12m No of storey 60 Core wall thickness 250mm Storey height 3m Floor slab 150mm 6-storey Module is considered for analysis Loads are applied as per the IS 875 code Case Study - II

40. Module Floor Height (m) P(Avg.) kn /m2 V(Avg.) kn /m M10 54-60 180 1.03 3.10 M9 48-54 162 1.01 3.05 M8 42-48 144 1.00 3.00 M7 36-42 126 0.98 2.95 M6 30-36 108 0.96 2.90 M5 24-30 90 0.93 2.80 M4 18-24 72 0.90 2.70 M3 12-18 54 0.88 2.65 M2 6-12 36 0.80 2.40 M1 1-6 18 0.76 2.30 A point atop each module is considered as tracking node, deflection, shear graphs are plotted for these points representing the module Varying Wind Load

41. Outcomes from study- More opening area Less Deflection 28 % less steel usage

42. - Rohit Kumar Singh et al. Analysis and design of concrete diagrid building and its comparison With conventional frame building A regular floor plan of 15m x 15m is considered in both buildings The design dead load and live load are 4.5 kN /m2 and 4 kN /m2 respectively analyzed for seismic zone V, with seismic parameter as per Indian code IS 1893(Part 1) : 2002 Case Study - III

43. 3D view of Conventional building 3D view of RCC Diagrid building Elevation of RCC Diagrid building

44. Comparison of max. Shear forces ( Fy ) and bending moments ( Mz ) in ground floor beams between conventional building and diagrid building

45. Shear Forces and Bending Moment in Beams

46. Shear Forces and Bending Moment in Diagonal Columns

47. Storey Drift comparison Structural performance: Diagrid building shows less lateral displacement and drift in comparison to conventional building. Material saving property: Although volume of concrete used in both building is approx. same, but diagrid shows more economical in terms of steel used. Diagrid building saves about 33% steel without affecting the structural efficiency. Study Output:

48. Better resistance to lateral loads: Due to diagonal columns on its periphery, diagrid shows better resistance to lateral loads and due to this, inner columns get relaxed and carry only gravity loads. Lesser Design Efforts: While in conventional building both inner and outer column are designed for both gravity and lateral loads.

49. - Prashant T G et al. Comparison Of Symmetric And Asymmetric Steel Diagrid Structures By Non-Linear Static Analysis 12 storey steel diagrid structure having height 36m and lateral dimensions as 18mX18m is considered for the analysis Nonlinear Static (Pushover) Analysis has been conducted Sl.No Building Details 1 Symmetric structure Model-1 2 Asymmetric structure Model-2 3 Plan dimensions of building 18m X 18m 4 Height of building 36 m 5 No. of stories 12 6 Storey height 3 m 7 Type of structure Steel diagrid structure 8 Type of analysis Nonlinear static analysis Case Study - IV

50. Asymmetric Structure Symmetric Structure

51. Asymmetric structure it can be observed that is pushover step 1 that assigned hinges are in a state of immediate occupancy. In step 2 it can be observed that some hinges shifts from immediate occupancy state to state of life safety and from figure that is step 3 it can be seen that some hinges shifts from life safety to collapse state. Symmetric structure it can be observed that pushover step 2 that the assigned hinges are in a state of immediate occupancy. In step 3 and step 4 one can observe that some hinges shifts from state of immediate occupancy to state of life safety due to the incremental increase in lateral load.

52. Pushover Analysis Steps

53. Examples of Diagrid Structures Capital Gate, Abu Dhabi O-14, Dubai COR, Miami Carpet, Russia

54. CCTV, China Coin Building, Dubai King’s Cross Station

55. As the lateral loads are resisted by diagonal columns, the top storey displacement is very much less in diagrid structure as compared to the simple frame building. The storey drift and storey shear is very much less for diagrid structural system Diagrid provide more resistance in the building which makes system more effective Diagrid structure provides more economy in terms of consumption of steel and concrete as compare to the simple fame building Diagrid structure provides more flexibility in planning interior space and façade of the building . Aesthetics and functionality of a building are improved simultaneously through diagrid. Conclusions

56. For every diagrid structure, it is recommended that diagrid structure is to be designed distinctively. Any methodology can be applied provided the maximum structural responses are within the limits Analysis of the Concrete diagrid structures is very little available and further research needs to be done towards it. Optimization techniques through different algorithms can be more advancely applied and research towards it is needed. They require skilled workers to work with nodes, fabrication is aslo needed hence expensive in construction

57. Future Scopes Diagrid Structures even due to their advantages and economy are handful in India due to demanding skillset of workers. The node connector can be fabricated in factories by training the workers and engineers the required knowledge and skills. The Diagrid Structures are to be compared with the available structural systems such as hexagrid and pentagrid Research in the analysis of Diagrid structure with core eccentricity is expected for practical applications of this structure.

58. Khushbu Jania , Paresh V. Patel, “Analysis and Design of Diagrid Structural System for High Rise Steel Buildings”, 3rd Nirma University International Conference on Engineering (NUICONE-2012 )   Mir M. Ali and Kyoung Sun Moon, “Structural Developments in Tall Buildings: Current Trends and Future Prospects”, Architectural Science Review, Volume 50.3, Pp 205-223 Terri Meyer Boake , Diagrids , “The New Stablity System: Combining Architecture with engineering”, Aei ( Asce ), 2013, P 578-583   Kyoung -Sun Moon, Jerome J. Connor and John E. Fernandez, “ Diagrid Structural Systems for Tall Buildings: Characteristics and Methodology for Preliminary Design”, Struct . Design Tall Spec. Build. 16, 205–230 (2007 ) Kyoung Sun Moon, “Structural Engineering for Complex-Shaped Tall Buildings”, ASCE, 2011 References

59. T. M. Boake ,” Diagrid Structures: Innovation and Detailing”, School Of Architecture, University Of Waterloo, 2012 Vinubhai Patel and N. Panchal , “ Diagrid Structural System: Strategies to Reduce Lateral Forces on Building”, IJRET, Vol. 5, 2012 Raghunath .D. Deshpande , Sadanand M. Patil , Subramanya Ratan , “Analysis and Comparison of Diagrid and Conventional Structural System”, IRJET, Volume: 02, Issue: 03, June - 2015 Khushbu D. Jani and Paresh V. Patel, “Design of Diagrid Structural System for High Rise Steel Buildings as Per Indian Standards”, Structures Congress, 2013 Dong- Kyu Lee, Uwe Starossek2 and Soo-Mi Shin,” Optimized Topology Extraction of Steel-Framed Diagrid Structure for Tall Buildings”, International Journal of Steel Structures June 2010, Vol 10, No 2, 157-164  

60. Kyoung Sun Moon,” Optimal Grid Geometry of Diagrid Structures for Tall Buildings”, Architectural Science Review, 2008, Volume 51.3, Pp 239-251   Rohit Kumar Singh, Dr. Vivek Garg , Dr. Abhay Sharma, “Analysis And Design Of Concrete Diagrid Building And Its Comparison With Conventional Frame Building”, International Journal Of Science, Engineering And Technology, Volume 2, Issue 6, August 2014 Raghunath .D. Deshpande, Sadanand M. Patil , Subramanya Ratan , “Analysis And Comparison Of Diagrid And Conventional Structural System”, International Journal Of Science, Engineering And Technology, Volume 02, Issue 03,June 2015

61. Thank You !